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Unformatted text preview: MATH 205 Quiz 2 June 8, 2009 NAME:
1. The coeﬃcient matrix of the following consistent system is already in reduced
row echelon form. Identify the dependent variables and the free variables. Solve
the system, and express your answer as a subset of R4 , so (x1 , x2 , x3 , x4 ) = . . . .
x1 − 2x2 + x4 = 0
x3 − 2x4 = 0 2. If A is the coeﬃcient matrix of the system in Problem 1, ﬁnd a spanning set
for the space of solutions. You should not repeat work done in Problem 1, which
already solves almost all of this question. 2 .
3. Find the coeﬃcient matrix A of the following system of equations, and ﬁnd its
inverse matrix A−1 . 3x1 − 4x2 = 1
2x1 − 5x2 = 3 4. Use your answer to problem 3 (the inverse matrix) to ﬁnd the solution to the
system of equations. ...
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- Fall '08